When Kirito logs in to ALO with his SAO account, all his SAO skills and points and even Yui's heart are loaded; so we can conclude that the same thing must have happened to his avatar, too. If so, why didn't Sugu recognize him and if not, why is that?

3 Answers
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When people were trapped in SAO, their avatars became exactly similar to their real-life bodies, so recognizing someone from real life was possible there.

Kirito at SAO:

Kirito in real life:

But in ALO, it's totally different.

See Sugu and leafa as an example:

Real Life:

ALO:

Kirito's avatar in ALO may resemble his character from SAO, yet it's still different.
A player with that avatar could look totally different in real life. And people that play MMORPG's are not use to talk about their real life at the game.

So, Leafa didn't recognize Kirito because there was no reason for her to do so in a game like ALO.

Adding to this - on SAO, people started off with whatever avatar they wanted. At a certain point their avatars were forced to their actual real-life look (around the time that it was revealed they could not log off etc...). It is reasonable to think that this, original avatar, was what Leafa/Sugu saw.
– OdedSep 18 '14 at 13:48

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@Maroon - just adding a possibility. In terms of visuals, it would be rather jarring if Kirito would have appeared as he was before the change on Alfheim and was therefore represented using his later appearance.
– OdedSep 18 '14 at 13:59

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I also remember when Kirito selected his race a voice said it was his appearance would be "generated" almost by random, either by total chance or from data confliction with his SAO Player Data Kirito looked similar to Post Death Game Start Kirito.
– Memor-XSep 18 '14 at 23:16

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Also to reaffirm the "A player with that avatar could look totally different in real life" part, at the start of the Death game remember how 2 characters reacted seeing their avatars change, one was playing as a young girl. Sugu probably just assumed she was playing with a guy and not a girl in a guy avatar (if Kirito was actually a girl and Sugu was still crushing on...*faints from over exposure to cute Shoujo Ai/Yuri*)
– Memor-XSep 18 '14 at 23:20

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ALO Avatars are randomly generated. Kirito created a new character, with a new avatar. A bug caused his SAO stats and items to transfer over, and overwrite most of his data; but his avatar didn't change. That said, the resemblance between his RL self and ALO Avatar is a result of the artists not wanting to confuse viewers. Even in Season 2, they didn't change the face of Kirito's GGO Avatar, even though the novels depict a VERY different face from his RL self. The similarities are to make sure people recognize him, but that clearly confuses some.
– TUSFSep 19 '14 at 0:04

When Kirito went onto ALO it said that his apearence will be randomised, however, since all of his data was transferred from SAO he looked the same as he did in SAO which was exactly how he looks in real life but when Sugu saw him she would not have thought it was her cousin because all the looks had been randomised.

Suguha didn't resemble her true self because it was a different machine in the anime but by the same creators... remember how they "asked them to touch themselves all over so they resemble the same?" Remember how there were mirrors and when they looked inside of them they looked exactly the same as what they look like in the real world? Maybe that's why. One, because f it's a different machine, then they might've forgot to make it so you had to touch yourself all over, two, because they didn't receive any mirrors in Alfheim.